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anonymous

  • one year ago

In parallelogram PQRS, find the height h. Then calculate the area of PQRS.

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  1. mathstudent55
    • one year ago
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    In a paralleogram, what do you know about opposite angles?

  2. anonymous
    • one year ago
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    |dw:1437449376951:dw|

  3. anonymous
    • one year ago
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    @mathstudent55 ∠R=45, ∠S=180-45=135, ∠P=45,and ∠Q=135.

  4. mathstudent55
    • one year ago
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    Correct. Opposite angles are congruent. |dw:1437450112404:dw|

  5. mathstudent55
    • one year ago
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    That makes the small triangle on the left side a 45-45-90 triangle.

  6. mathstudent55
    • one year ago
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    |dw:1437450166044:dw|

  7. mathstudent55
    • one year ago
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    Since you have a 45-45-90 triangle, you can use the ratio of the length of the sides of a 45-45-90 triangle to find h.

  8. mathstudent55
    • one year ago
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    Do you know the ratio of the sides of a 45-45-90 triangle?

  9. anonymous
    • one year ago
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    1 to 1

  10. anonymous
    • one year ago
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    \[\sqrt{2}\]

  11. mathstudent55
    • one year ago
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    Yes, \(1 : 1 : \sqrt 2\) The hypotenuse is \(\sqrt 2\) times the length of either leg. The legs are congruent. The height of the parallelogram is the leg of the right triangle. What is the length of the leg?

  12. anonymous
    • one year ago
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    8

  13. mathstudent55
    • one year ago
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    Correct. Now you know the height of the parallelogram is 8. Do you know how to find the area of a parallelogram?

  14. mathstudent55
    • one year ago
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    \(\Large A_{parallelogram} = bh\) where b = length of base, and h = height.

  15. mathstudent55
    • one year ago
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    You were given a base of 20 cm, and you calculated a height of 8 cm.

  16. anonymous
    • one year ago
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    A=bh. So A=20x8= 160cm^2

  17. mathstudent55
    • one year ago
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    @SimiYami Do you understand how to find the area?

  18. anonymous
    • one year ago
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    Yes, thank you for the help @mathstudent55. This is the exact answer in my book :D

  19. mathstudent55
    • one year ago
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    You're welcome.

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